Compactly Supported Basis Functions as Support Vector Kernels for Classification.

Area of Science:

• Machine Learning
• Signal Processing
• Kernel Methods

Background:

• Wavelet kernels are used in support vector regression and classification.
• Existing wavelet kernels often bypass the embedding space inner product, resembling radial basis function kernels.
• Wavelet analysis typically requires temporal or spatial data relationships.

Purpose of the Study:

• To develop a new family of wavelet kernels applicable to general datasets.
• To enable the interpretation of general data vectors as observations of a continuous signal.
• To improve the performance of machine learning models using novel wavelet kernels.

Main Methods:

• Ordering general dataset features to establish statistical relationships between consecutive features.
• Interpreting data vectors as sampled hypothetical continuous signals.
• Approximating signals using compactly supported basis functions.
• Employing the L2 embedding space inner product for kernel construction.

Main Results:

• A novel family of wavelet kernels was successfully derived.
• Empirical evaluations demonstrated a clear performance advantage for the proposed kernels.
• The new kernels effectively utilize the statistical relationships within ordered general datasets.

Conclusions:

• The proposed method of ordering features and employing the L2 inner product yields effective wavelet kernels.
• This approach expands the applicability of wavelet kernels to general datasets beyond traditional temporal or spatial data.
• The novel wavelet kernels offer superior performance in machine learning tasks.